新的加权谱几何平均和量子散度

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2025-07-28 DOI:10.1016/j.laa.2025.07.025

Miran Jeong , Sejong Kim , Tin-Yau Tam

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引用次数: 0

摘要

最近引入了一类新的加权谱几何均值。本文从Löwner阶、算子范数和迹的角度给出了它的不等式。此外，我们建立了新的光谱几何平均值与r相对算子熵之间的对数多数化关系。我们还研究了由算术平均值与新谱几何平均值之间的迹值之差给出的量的量子散度。最后，我们研究了使给定变量的量子散度加权和最小的质心。

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New weighted spectral geometric mean and quantum divergence

A new class of weighted spectral geometric means has recently been introduced. In this paper, we present its inequalities in terms of the Löwner order, operator norm, and trace. Moreover, we establish a log-majorization relationship between the new spectral geometric mean and the Rényi relative operator entropy. We also study the quantum divergence of the quantity, given by the difference of trace values between the arithmetic mean and new spectral geometric mean. Finally, we study the barycenter that minimizes the weighted sum of quantum divergences for given variables.

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来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.